Multivariate Statistical Process Control Charts: An Overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

Optimal filter design approaches to statistical process control for autocorrelated processes

Statistical Process Control (SPC), and in particular control charting, is widely used to achieve and maintain control of various processes in manufacturing. A control chart is a graphical display that plots quality characteristics versus the sample number or the time line. Interest in effective implementation of control charts for autocorrelated processes has increased in recent years. However, because of the complexities involved, few systematic design approaches have thus far been developed. Many control charting methods can be viewed as the charting of the output of a linear filter applied to the process data. In this dissertation, we generalize the concept of linear filters for control charts and propose new control charting schemes, the general linear filter (GLF) and the 2nd-order linear filter, based on the generalization. In addition, their optimal design methodologies are developed, where the filter parameters are optimally selected to minimize the out-of-control Average Run Length (ARL) while constraining the in-control ARL to some desired value. The optimal linear filters are compared with other methods in terms of ARL performance, and a number of their interesting characteristics are discussed for various types of mean shifts (step, spike, sinusoidal) and various ARMA process models (i.i.d., AR(1), ARMA(1,1)). Also, in this work, a new discretization approach for substantially reducing the computational time and memory use for the Markov chain method of calculating the ARL is proposed. Finally, a gradient-based optimization strategy for searching optimal linear filters is illustrated

Practical Design of Generalized Likelihood Ratio Control Charts for Autocorrelated Data

Control charts based on Generalized Likelihood Ratio (GLR) tests are attractive from both a theoretical and practical point of view. In particular, in the case of an autocorrelated process, the GLR test uses the information contained in the time-varying response after a change and, as shown by Apley and Shi, is able to outperfom traditional control charts applied to residuals. In addition, a GLR chart provides estimates of the magnitude and the time of occurrence of the change. In this paper, we present a practical approach to the implementation of GLR charts for monitoring an autoregressive and moving average process assuming that only a Phase I sample is available. The proposed approach, based on automatic time series identification, estimates the GLR control limits via stochastic approximation using bootstrap resampling. Thus, it is able to take into account the uncertainty about the underlying model. A Monte Carlo study shows that our methodology can be used to design in a semi-automatic fashion a GLR chart with a prescribed rate of false alarms when as few as 50 Phase I observations are available. A real example is used to illustrate the designing procedure

Enhanced Monitoring Using Multiscale Exponentially Weighted Moving Average Control Charts

The exponentially weighted moving average (EWMA) method is a widely used univariate process monitoring technique. This conventional EWMA technique is normally designed to optimize the out of control average run length (ARL1) specific to a fixed in control average run length (ARL0). This design procedure of EWMA technique is based on some assumptions – the evaluated process residuals are Gaussian, independent and contain moderate level of noise. Violation of these assumptions may adversely affect its fault detection abilities. Wavelet based multiscale representation of data is a powerful data analysis tool and has inherent properties that can help deal with these violations of assumptions, which thus improve the performance of EWMA through satisfying its assumptions. The main purpose of this work is to develop a multiscale EWMA technique with improved performance over the conventional technique and establish a design procedure for this method to optimize its parameters by minimizing the out of control average run length for different fault sizes and using a specified in control average run length assuming that the residuals are contaminated with zero mean Gaussian noise. Through several comparative studies using Monte Carlo simulations, it has been shown that the multiscale EWMA technique provides a better performance over the conventional method. Multiscale EWMA is shown to provide smaller ARL1 and missed detection rate with a slightly higher false alarm rate compared to the conventional EWMA technique not only when both the techniques are designed to perform optimally but also when data violate the assumptions of the EWMA chart. The advantages of the multiscale EWMA method over the conventional method are also illustrated through their application to monitor a simulated distillation column

Integrated Projection and Regression Models for Monitoring Multivariate Autocorrelated Cascade Processes

This dissertation presents a comprehensive methodology of dual monitoring for the multivariate autocorrelated cascade processes using principal component analysis and regression. Principle Components Analysis is used to alleviate the multicollinearity among input process variables and reduce the dimension of the variables. An integrated principal components selection rule is proposed to reduce the number of input variables. An autoregressive time series model is used and imposed on the time correlated output variable which depends on many multicorrelated process input variables. A generalized least squares principal component regression is used to describe the relationship between product and process variables under the autoregressive regression error model. The combined residual based EWMA control chart, applied to the product characteristics, and the MEWMA control charts applied to the multivariate autocorrelated cascade process characteristics, are proposed. The dual EWMA and MEWMA control chart has advantage and capability over the conventional residual type control chart applied to the residuals of the principal component regression by monitoring both product and the process characteristics simultaneously. The EWMA control chart is used to increase the detection performance, especially in the case of small mean shifts. The MEWMA is applied to the selected set of variables from the first principal component with the aim of increasing the sensitivity in detecting process failures. The dual implementation control chart for product and process characteristics enhances both the detection and the prediction performance of the monitoring system of the multivariate autocorrelated cascade processes. The proposed methodology is demonstrated through an example of the sugar-beet pulp drying process. A general guideline for controlling multivariate autocorrelated processes is also developed

Seasonal ARMA-based SPC charts for anomaly detection: Application to emergency department systems

Monitoring complex production systems is primordial to ensure management, reliability and safety as well as maintaining the desired product quality. Early detection of emergent abnormal behaviour in monitored systems allows pre-emptive action to prevent more serious consequences, to improve system operations and to reduce manufacturing and/or service costs. This study reports the design of a new methodology for the detection of abnormal situations based on the integration of time-series analysis models and statistical process control (SPC) tools for the joint development of a monitoring system to help supervising of the behaviour of emergency department services (EDs). The monitoring system developed is able to provide early alerts in the event of abnormal situations. The seasonal autoregressive moving average (SARMA)-based exponentially weighted moving average (EWMA) anomaly detection scheme proposed was successfully applied to the practical data collected from the database of the paediatric emergency department (PED) at Lille regional hospital centre, France. The method developed utilizes SARMA as a modelling framework and EWMA for anomaly detection. The EWMA control chart is applied to the uncorrelated residuals obtained from the SARMA model. The detection results of the EWMA chart are compared with two other commonly applied residual-based tests: a Shewhart individuals chart and a Cumulative Sum (CUSUM) control chart